Very recently, great progress has been made in developing a neuron computer. Both a Hopfield type and also a Rumelhart type are known as typical neurocomputers.
A neurocomputer is designed as a brain model of a human. For instance, several thousands of million of neurons (neurons cells) which own two states, i.e., under inert state when an input reaches a certain threshold value, and under active condition when the input exceeds this threshold value, are combined with each other for operation purposes, whereby this neurocomputer may process optimum combination problems and recognition which are not preferably processed by the presently available computers.
The previously described Hopfield type neurocomputer is suitable for solving the optimum combination problem. It should be noted that the optimum combination problem implies that combinations are obtained by which a certain condition of articles having such discrete values as "1" and "0" is minimized (or maximized). Since no generic method for solving this problem has been known in prior art, it is extremely difficult to solve a problem having a large scale.
To the contrary, in U.S. Pat. No. 4,660,166 and the like, Hopfield has disclosed that the traveling salesman problem which is the most difficult combination problem to be solved could be solved by the neuronal computation at a high velocity, and the solution close to the optimum solution could be obtained. It should be understood that "this traveling salesman problem" is to obtain the shortest traveling path routing n cities under such constraint that the salesman travels the respective cities only one time. With respect to n cities, there are combinations of n!/2n=n(n-1) - - - 2.1/2n.
In accordance with Hopfield, n pieces of neurons correspond to each of n cities (accordingly, n.sup.2 pieces of neurons are employed in total), and when the i-th neuron of the respective cities becomes active, it implies that the salesman visits this town at an i-th traveling sequence. The combinations between the respective neurons are determined under both constraint condition that he passes through the respective cities only once, and shortest distance condition. A summation of these conditions is defined as energy, and then operation of neurons is assumed that this energy becomes low in a lapse of time. As a result, when a proper value between the active state (1) and inactive state (0) is set to each neuron, the energy is lowered in a lapse of time, and the neuronal computation is stopped where the energy is locally minimized. "n" pieces of neurons are brought into active states among n.sup.2 pieces of neurons so that the constraint conditions are satisfied and a solution close to the minimum distance can be obtained.
Now, the above-described contents will be described with employing an energy function. It is assumed that an energy value "E" is given as follows: ##EQU1## It should be noted that x, T and b indicate an n-dimensional variable vector, an nxn-dimensional coefficient matrix, and an n-dimensional input vector, respectively, and "t" indicates a symbol of transposition. Each of symbols is expressed by: ##EQU2## Assuming now that "T" is a symmetric matrix, namely T.sub.ij =T.sub.ji. It has been described that this energy E is obtained as follows. That is, when "X" is equal to a value of "0" or "1", otherwise "-1" or "1", this X for minimalizing E is calculated by solving the following differential equation: ##EQU3##
It should be understood that correspondence to a neuron is as follows. An output of i-th neuron among "n" pieces of neurons corresponds to Xi; an input corresponds to a constant input bi; an input from the i-th neuron corresponds to T.sub.ij X.sub.j ; and also an output itself inputted thereto corresponds to T.sub.i X.sub.i. Accordingly, T.sub.ij indicates a strength of an input combination from a j-th neuron to an i-th neuron. In particular, T.sub.il represents a strength of an input combination of the output for the i-th neuron supplied thereto.
Since, as the method for solving the large-scale optimum combination problems, no method with a better efficiency has been known, and thus a lengthy time is required so as to solve such large-scale problems, there could be simply obtained the solution near the optimum solution by solving the equation (2).
However, the solution obtained by way of the above-described conventional method corresponds to a minimal value, but not a minimum value. Although convergence characteristic thereof has been described to some extent in Technical Research Report by Electronic Information Communication Society, PRU 88-6 (1988), pages 7 to 14, no definite solution could be obtained. This implies such a trial and error condition that no clear answer is made on how to control the neurocomputer.
Furthermore, in general, there are some cases in which an inequality constraint is given in combination problems. However, the above-described prior art cannot be applied thereto.